like a shot vs right away

like a shot and right away both are adverbs.

Word	Noun	Adjective	Verb	Adverb
like a shot	No	No	No	Yes
right away	No	No	No	Yes

As adverbs, like a shot and right away are synonyms defined as:

like a shot and right away: without delay or hesitation; with no time intervening

Other synonyms of like a shot include at once, directly, forthwith, immediately, instantly, now, straight off, straightaway.

like a shot (adverb)	right away (adverb)
without delay or hesitation; with no time intervening	without delay or hesitation; with no time intervening
	at once (usually modifies an undesirable occurrence)